Dirty water is the most common water in the game, and is drawn from the tainted lakes and rivers. Unlike purified water, this will give you radiation, which can be cured for a fee by a doctor or by using RadAway.
Purified water is water that has been purged of any radiation, making it one of the only "clean" sources of water in the wasteland. It is not quite as common in the Capital Wasteland as it is in the Mojave, but the water is still rather common, often being found in first aid kits and more advanced settlements.
Aqua Cura is regular irradiated water disguised in an Aqua Cura bottle that Griffon sells in Underworld to cure a plethora of illnesses that ghouls often suffer from. Griffon also takes the real Aqua Pura and sells it to other wastelanders at an inflated price.
Each bottle of purified water appears to feature the text "'H²O" hand written on the label on the side of the bottle. This format is incorrect (at least according to IUPAC nomenclature) as in chemical formula numbers are written in subscript, not superscript. If read literally, the chemical formula H²O would mean there is one hydrogen and one oxygen isotope that contains two neutrons (instead of the standard eight). This would leave the oxygen extremely unstable and radioactive with a half life that would be so small that it would not be measurable.